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Extention of Totient Function to Reals

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#number-theory #riemann-zeta #totient-function
253
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On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

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#number-theory #prime-factorization #totient-function #perfect-numbers
48
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Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

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#sequences-and-series #analytic-number-theory #irrational-numbers #rational-numbers #totient-function
258
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RSA decryption coefficient

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#cryptography #totient-function
65
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An asymptotic about the recurrence $a_{n+1}=n\varphi(a_n)+a_{\varphi(n)}$, with $a_1=1$ and being $\varphi(m)$ the Euler's totient function

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#sequences-and-series #recurrence-relations #asymptotics #totient-function
76
Views

Euler Totient Integer Remainder Sum Lemma

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#elementary-number-theory #totient-function
69
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Totient values of consecutive positive integers forming a pythagorean triple

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#number-theory #elementary-number-theory #totient-function #pythagorean-triples
57
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A conjecture about Euler's function

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#elementary-number-theory #totient-function
63
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Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

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#elementary-number-theory #modular-arithmetic #divisibility #totient-function #divisor-sum
90
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Calculate modulo solution of a number with a high exponent

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#discrete-mathematics #modular-arithmetic #cryptography #totient-function
144
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Does a number have a primitive root if and only if φ(n)=λ(n)?

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#group-theory #number-theory #elementary-number-theory #totient-function #primitive-roots
66
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Do $4$ consecutive positive integers with square totient-value exist?

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#elementary-number-theory #totient-function
105
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Conditions for computing $n$ given $\varphi\left(n\right)$

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#elementary-number-theory #prime-numbers #totient-function
282
Views

Find solutions to $\varphi\left(n\right)=2^{32}$

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#elementary-number-theory #prime-numbers #totient-function
201
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Are there further primes of the form $\varphi(n)^{\varphi(\varphi(n))}+1$?

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#number-theory #elementary-number-theory #prime-numbers #totient-function

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